Discrete element method modeling of inherently anisotropic rocks under uniaxial compression loading

A new numerical approach is proposed in this study to model the mechanical behaviors of inherently anisotropic rocks in which the rock matrix is represented as bonded particle model, and the intrinsic anisotropy is imposed by replacing any parallel bonds dipping within a certain angle range with smooth‐joint contacts. A series of numerical models with β = 0°, 15°, 30°, 45°, 60°, 75°, and 90° are constructed and tested (β is defined as the angle between the normal of weak layers and the maximum principal stress direction). The effect of smooth‐joint parameters on the uniaxial compression strength and Young's modulus is investigated systematically. The simulation results reveal that the normal strength of smooth‐joint mainly affects the behaviors at high anisotropy angles (β > 45°), while the shear strength plays an important role at medium anisotropy angles (30°–75°). The normal stiffness controls the mechanical behaviors at low anisotropy angles. The angle range of parallel bonds being replaced plays an important role on defining the degree of anisotropy. Step‐by‐step procedures for the calibration of micro parameters are recommended. The numerical model is calibrated to reproduce the behaviors of different anisotropic rocks. Detailed analyses are conducted to investigate the brittle failure process by looking at stress‐strain behaviors, increment of micro cracks, initiation and propagation of fractures. Most of these responses agree well with previous experimental findings and can provide new insights into the micro mechanisms related to the anisotropic deformation and failure behaviors. The numerical approach is then applied to simulate the stress‐induced borehole breakouts in anisotropic rock formations at reduced scale. The effect of rock anisotropy and stress anisotropy can be captured. Copyright © 2015 John Wiley & Sons, Ltd.     

共面闭合断续节理岩体强度特性直剪试验研究

为了揭示不同裂纹贯通模式的细观演化机理,采用颗粒流程序(PFC)模拟含平行双裂隙石膏试样的单轴压缩试验。对双预制裂隙在不同相对位置时试样内出现的裂纹贯通模式进行分类,并对不同贯通模式形成过程中预制裂隙周围的力链和颗粒位移场进行分析。研究发现预制裂隙的相对位置会改变压缩过程中其周围的接触力分布以及颗粒位移趋势,进而影响预制裂隙端部以及岩桥区域裂纹的扩展路径。当两预制裂隙几乎共面时,在岩桥区域存在接触力集中情况,岩桥区域首先出现微张拉裂纹,随着加载,这些微张拉裂纹逐渐演化为宏观剪切带并连接两个预制裂隙端点,形成Ⅰ型贯通。当岩桥倾角较大且两个预制裂隙不重叠时,岩桥区域的接触力集中程度增大,岩桥区域首先出现竖向的微张拉裂纹并演化为竖向的宏观裂纹连接两个预制裂隙端点,导致Ⅱ或Ⅶb型贯通。当两个预制裂隙的端部部分重叠时,由于应力屏蔽效应,重叠端部的压缩接触力集中程度小于未重叠端部,导致翼裂纹成为主导贯通的裂纹。当两个预制裂隙在竖直方向完全重叠时,两预制裂隙同侧端点之间的接触力集中导致出现由压致拉的张拉裂纹连接预制裂隙同侧端点,形成Ⅴ型贯通。出现Ⅱ、Ⅴ和Ⅶb型贯通试样的微裂纹数量曲线呈现阶梯状增长的趋势,表明这3类贯通中宏观裂纹的扩展是由应变能的突然释放导致的。     

Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression

The strength and deformability of rock masses transected by non-persistent joints are controlled by complex interactions of joints and intact rock bridges. The emergence of synthetic rock mass (SRM) numerical modelling offers a promising approach to the analysis of rock masses, but has not been rigorously compared with actual physical experiments. In this work, SRM modelling by the discrete element software PFC3D is used to investigate the effect of geometric parameters of joints on the rock mass failure mechanism, unconfined compressive strength and deformation modulus. Firstly, a validation study is undertaken to investigate the ability of SRM modelling to reproduce rock mass failure modes and strength as determined by uniaxial and biaxial compression testing in the laboratory. The numerical analyses agree well with physical experimentation at low confining pressure. A sensitivity study is then undertaken of the effect of joint configuration parameters on the failure mode, unconfined compressive strength and deformation modulus of the rock mass. Five failure modes are predicted to occur: intact rock, planar, block rotation, step-path and semi-block generation. It is found that the failure mode is determined principally by joint orientation and step angle and the joint orientation with respect to principal stress direction is the parameter with the greatest influence on rock mass properties.     

Influence of the intermediate principal stress and principal stress direction on the mechanical behavior of cohesionless soils using the discrete element method

In this paper, the Discrete Element Method (DEM) is employed to numerically explore the response of hollow cylinder specimens of granular soils under complex stress paths. Two series of numerical tests are conducted to clarify the effects of the principal stress direction α and the intermediate principal stress through the b-value on the mechanical response of granular materials. The effects of α and b-value on the non-coaxiality of the principal stress and the principal plastic strain increment directions are investigated. It is observed that b-value and α significantly affect the non-coaxial behavior of granular materials. Finally, the results are discussed and compared with those obtained from physical laboratory tests.     

基于离散元数值方法的砂土小应变弹性特性探讨

土体在非常小应变（小于10?6）时表现为线弹性。以往大量试验研究表明,土体的弹性特性主要受到土体有效围压、孔隙比、颗粒级配和试样制备方法等影响。通过离散元方法模拟Duffy和Mindlin中的物理试验,建立球形颗粒规则排列的三维模型,继而进行小变形条件下的数值加载试验来确定弹性特性,并从细观层面揭示决定土体弹性特性的内在因素。模拟结果表明：粒状土的弹性模量取决于土体的颗粒接触配位数、法向接触力的大小和分布,跟宏观土体孔隙比、有效围压作用相对应。弹性模量应力指数n高于Hertz-Mindlin接触法则对应的1/3,主要是由于应力增加过程中配位数的增加和接触力趋于更均匀导致。同时,泊松比也随着配位数的增加而减小,并非保持不变,跟试验结果趋势一致。     

基于扩展有限元的压剪复合断裂数值分析

针对岩石类材料压剪破坏,国内外学者做了大量真实岩石和模型材料的试验,并进行相应的数值模拟工作。但由于试验结果往往具有很强的离散性,且对影响试验结果的各因素缺乏系统地理论分析,加之传统常规有限元在处理裂纹这类强不连续问题时存在很大的困难,如在裂尖附近的高应力区需要剖分令人难以接受的密度的网格,同时在模拟裂纹生长时还需要对网格进行重新剖分,操作繁琐复杂,效率极低,因此,针对压剪复合断裂翼裂纹扩展规律的研究始终没有取得令人满意的成果。对原生裂纹的几何形态,主裂纹面与其间填充物的相互作用对翼裂纹起裂角的影响做了系统的理论分析,并利用扩展有限元对翼型裂纹扩展全过程进行数值模拟,与理论分析结果对比,吻合良好。相关成果为以后针对压剪复合断裂的研究提供了理论分析框架,同时对今后相关试验的开展具有理论指导作用     

碳酸盐岩水热协同混合溶蚀作用机理的数值试验研究

在封闭岩溶水系统中,当水化学组分或温度不同的饱和地下水发生混合时,将增加地下水的碳酸盐矿物溶解度,产生新的溶蚀能力。为了揭示常见地下水混合情况下的饱和溶液混合溶蚀和温度混合溶蚀协同作用机理,文章采用水文地球化学软件PHREEQC模拟了土壤入渗水与浅层地下水、深循环热水与浅层地下水、深部流体与浅层地下水混合条件下的碳酸钙溶蚀反应,讨论了地下水温度、二氧化碳分压（$ {P}_{{\text{CO}}_{\text{2}}} $）以及端元溶液混合比例对水热协同混合溶蚀作用强度的影响。研究结果表明：天然地下水混合条件下的水热协同混合溶蚀作用能够增加已经饱和地下水的溶蚀能力,混合溶液补充溶蚀能力由强到弱依次为：深部流体与浅层地下水混合,深循环热水与浅层地下水混合,土壤入渗水与浅层地下水混合;在土壤入渗水与浅层地下水混合、深循环热水与浅层地下水混合情况下,水热协同混合溶蚀作用以饱和溶液混合溶蚀作用为主,温度混合溶蚀作用为辅,在深部流体与浅层地下水混合条件下,虽然温度变化会使得饱和溶液析出碳酸钙沉淀,但混合溶液整体上仍表现为较强的侵蚀性。岩溶水系统中的水热协同混合溶蚀作用强度受温度和$ {P}_{{\text{CO}}_{\text{2}}} $变化同步控制,端元溶液温度和$ {P}_{{\text{CO}}_{\text{2}}} $差异越大,其水热协同混合溶蚀能力越强,端元溶液混合比例接近时,最有利于碳酸钙溶解。研究成果揭示饱和溶液溶蚀和温度混合溶蚀的协同作用机理,能够为碳酸盐岩地区水、地热、油气资源储存空间勘探提供理论依据。     

Major and trace element, and Sr-Nd isotope constraints on the origin of Paleogene volcanism in South China prior to the South China Sea opening

Paleogene volcanic rocks crop out in three sedimentary basins, namely, Sanshui, Heyuan and Lienping, in the attenuated continental margin of south China. Lavas from the Sanshui basin which erupted during 64-43 Ma are bimodal, consisting of intraplate tholeiitic basalt and trachyte/rhyolite associations. Similar to Cretaceous A-type granites from the nearby region, the felsic member shows peralkaline nature [Na₂O + K₂O ≈ 10–12%; (Na + K)/Al≈ 0.98−1.08], general enrichment in the incompatible trace elements and significant depletion in Ba, Sr, Eu, P and Ti. Although both types of the Sanshui lavas have rather uniform Nd isotope compositions [_Nd(T) ≈ +6 to +4]that are comparable to Late Cenozoic basalts around the South China Sea, the felsic rocks possess apparently higher initial Sr isotope ratios (I_Sr up to 0.713) and form a horizontal array to the right in the Nd vs. Sr isotope plot. Closed system differentiation of mantle-derived magmas in a ‘double diffusive’ magma chamber is considered for the bimodal volcanism, in which the trachytes and rhyolites represent A-type melts after extensive crystal fractionation in the upper portion of the chamber. Such A-type melts were later contaminated by small amounts (1–3%) of upper crustal materials during ascent. On the other hand, composition of lavas in the other two basins varies from tholeiitic basalt to andesite. Their Sr and Nd isotope ratios [I_Sr ≈ 0.705 to 0.711; _Nd(T) ≈ +1 to − 5] and generally correlative Nb-Ta depletions suggest a distinct magma chamber process involving fractional crystallization concomitant with assimilation of the country rock. We conclude that these Paleogene volcanic activities resulted from the lithospheric extension in south China that migrated southwards and eventually led to opening of the South China Sea during 30-16 Ma.     

热应力影响下干热岩水压致裂数值模拟

干热岩水压致裂过程中低温诱导热应力与注入水压共同影响裂缝的萌生与扩展。首先通过THM耦合分析了低温压裂液注入过程中注入水压与热应力的相互作用及其对裂缝萌生的影响,随后建立描述岩石细观结构的THMD耦合模型对热应力影响下高温岩石水压致裂过程进行初探。结果表明：低温压裂液注入高温岩石产生的热应力包括岩石自身温度梯度形成的热应力与岩石颗粒非均匀膨胀导致的热应力,并在井筒周围呈现为拉应力。高注入压力将抑制热应力导致的多裂缝萌生,井筒附近热应力的存在对注入压力也具有削弱作用。基岩温度升高,裂缝萌生阶段更多裂缝在井筒附近起裂,缝网沿最大地应力方向的扩展速度减慢,但改造规模增加,同时多裂缝的存在也使得裂缝延伸压力增加。     

孔隙填充型能源土的宏微观力学特性真三轴试验离散元分析

天然气水合物沉积物因其作为绿色新型能源且具有广阔的开发前景而备受全球瞩目。水合物在水合物沉积物（俗称能源土试样）中有不同的赋存型式,如孔隙填充型和胶结型等。针对孔隙填充型水合物的赋存形态,生成特定饱和度的能源土试样。开展了同一 平面上不同中主应力系数（b = 0、0.25、0.50、0.75、1.00）的真三轴排水试验的三维离散元模拟,将微观参数接触组构及剪切滑移率的演化规律与材料的宏观力学响应相结合,分析了中主应力对孔隙填充型能源土的宏微观力学响应的影响。结果表明：强接触处组构张量的大、中、小主值随b的变化规律与大、中、小主应力及大、中、小主应变随b的变化规律表现出良好的相关性。三向应力状态下的破坏强度接近Lade-Duncan破坏准则。能源土试样剪切滑移率随着中主应力系数的增大而增大;当处于三轴拉伸状态时,试样的剪切滑移率最大。     

干湿循环作用下污泥固化土三维力学特性研究

采用自主研发的新型固化剂对天津城市污泥进行固化处理,通过GCTS真三轴仪对污泥固化土进行不固结不排水试验,探讨其在干湿循环作用下的应力-应变特征和强度指标变化规律。试验结果表明：污泥固化土应力-应变曲线在初始阶段近似表现为线性关系,同等条件下,破坏应力随中主应力比b的增大而增大;相同b值下,破坏应力随干湿循环次数的增大而逐渐减小。经过干湿循环1,3,5,7,10次之后,不同围压下污泥固化土的破坏应力值均呈现下降趋势。当循环次数超过5次后,其降低幅度趋于平缓。在b值较小、循环次数小于3时,应力-应变曲线产生应变软化现象,随着围压和b值的增大表现为硬化型。污泥固化土c、φ值随干湿循环次数的增大呈现出降低趋势,并最终趋于稳定。在此基础上,对不同中主应力比条件下的c、φ值变化规律进行分析,分别建立其与干湿循环次数和中主应力比之间的关系式,并构建出能够考虑不同围压及中主应力比影响的初始弹性模量Ei和主应力差渐近值（σ1−σ3）ulti预测公式。     

高渗透压脆性岩石蠕变宏−细观力学模型研究

高渗透压对深部地下工程脆性岩石蠕变力学特性有着重要影响。然而,能够解释高渗透压作用脆性岩石完整减速、稳态及加速三级蠕变过程中,细观裂纹扩展与宏观变形关系的宏细观力学模型研究很少。基于考虑含有初始裂纹与新生成翼型裂纹影响的裂纹尖端应力强度模型,引入渗透水压与初始裂纹及新生成翼型裂纹之间的力学关系,建立了考虑渗透水压作用的裂纹尖端应力强度模型;然后结合亚临界裂纹扩展法则,与裂纹及应变损伤关系模型,推出了考虑渗透水压影响的脆性岩石蠕变裂纹扩展与宏观变形关系的宏细观力学模型。当施加轴向应力小于岩石裂纹启裂应力时,岩石近似表现为线弹性变形;当施加轴向应力大于裂纹启裂应力且小于岩石峰值强度,岩石表现为塑性蠕变变形。研究了不同渗透压作用下,分级轴向应力加载岩石蠕变应变时间演化曲线,并通过试验结果验证了模型的合理性。分别讨论了恒定渗透压与分级渗透压,对脆性岩石蠕变过程中裂纹长度、裂纹扩展速率、轴向应变及轴向应变率的影响。该模型为高渗透压深部地下工程围岩稳定性评价提供了重要理论依据。     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.     

基于考虑动力本构的连续−非连续方法的单轴压缩岩样开裂过程模拟

动载作用下岩石的破坏规律研究对于众多地质灾害的机制分析和预防具有重要的理论及实际意义。鉴于数值模拟研究的优势,应大力发展适于岩石动力断裂过程模拟的数值方法。在自主开发的拉格朗日元与离散元耦合连续−非连续方法的基础上,采用朱−王−唐本构模型取代了广义胡克定律,发展了考虑动力本构的连续−非连续方法,其正确性通过模拟不同加载速度时砂岩试样的单轴压缩试验进行了验证。通过统计裂缝区段数目随着岩样的纵向应变的演化规律,并监测岩样左、右对称线上多个测点的最小主应力的演化规律,开展了不同加载速度时单轴压缩花岗岩试样的变形−开裂过程研究,阐明了岩样的开裂机制。研究发现,剪裂缝以雁列式展布,整体上形成剪切带。随着时步数目的增加,各测点的最小主应力均呈波动下降−震荡上升的变化趋势。震荡上升阶段对应岩样的应变软化阶段。测点分离后最小主应力的震荡幅度较大,这是由于节点分离和单元接触激发了较大的应力波。剪切带尖端的最小主应力集中会使测点发生剪切分离。当岩样的三角块向下楔入时,下方测点的应力状态类似于紧凑拉伸试验进而发生拉伸分离。     

采深和松散层厚度对开采沉陷地表移动变形影响的数值模拟研究

文章以山西霍州辛置煤矿2204工作面为试验研究基地,采用岩石破裂软件RFPA2D模拟开采沉陷过程,研究煤层采动后地表移动及变形的规律;系统地分析了采深采厚比对地表移动及变形的影响。     

Numerical investigation of the effect of volatilization and the supercritical state of pore water on maturation of organic matter in the vicinity of igneous intrusions

This study presents a numerical investigation of the effect of volatilization and the supercritical state of pore water on maturation of organic matter in host rocks based on the heat flow models assuming the instantaneous and finite-time intrusion mechanisms of magma. A 15 m thick, well-dated basic sill in the DSDP 41-368 hole near Cape Verde Rise, eastern Atlantic is selected as an example due to the sufficient thermophysical parameters of rocks and the definite burial and thermal history of the shale host rocks. Results indicate: (1) The effect of the temperature-dependent thermal properties of pore water at a hydrostatic pressure of 414 bar on the predicted vitrinite reflectance (Rr) is less than 0.1% no matter which intrusion mechanism of magma is assumed and can hence be ignored reasonably; (2) The consideration of volatilization of pore water can reduce the predicted Rr of host rocks significantly. In case of the instantaneous intrusion mechanism, the maximum deviation of the predicted Rr caused by pore-water volatilization reaches 1.3% at the location of half the sill thickness away from the contact (i.e. X/D = 0.5), and the deviation above 0.5% can occur in the region from 0.3 to 1.0 in the form of X/D. In case of the finite-time intrusion mechanism, the maximum deviation of the predicted Rr due to pore-water volatilization attains 1.15% at X/D = 0.25, and the region where the deviation is larger than 0.5% lies between 0.15 and 0.6 in the form of X/D; (3) If hydrothermal convection in the host rocks is allowed for, the predicted Rr of the overlying host rocks is less than that of the underlying host rocks at the same X/D in the inner region of the contact aureole of igneous intrusions, whereas the phenomenon is converse in the outer region. In contrast, the measured Rr profile shows that at the same X/D, Rr of the overlying host rocks is totally higher than that of the underlying host rocks. Thus, it is not the hydrothermal convection in the overlying host rocks that resulted in the asymmetry of the current Rr profiles below and above the sill; (4) The predicted Rr based on the heat conduction model assuming the finite-time intrusion mechanism and pore-water volatilization matches well with the measured one out of the region where the Rr geothermometer is unreliable due to the effect of volatilization of pore water. This demonstrates that the finite-time intrusion mechanism of magma, together with pore-water volatilization, possibly represents natural conditions.     

等压扩散下CO2对不同变质程度煤中CH4置换效应的影响

为了研究等压扩散条件下不同变质程度煤中CO₂置换CH₄特征规律,选择无烟煤、瘦煤和气肥煤3种煤样,进行了不同等压扩散压力下的等压扩散置换实验。实验结果表明：随着煤变质程度的增加煤吸附CH₄和CO₂的能力表现出逐渐增强的趋势,且CO₂的吸附量大于CH₄的吸附量;随着实验点扩散压力的增加,CO₂对CH₄的绝对置换量和置换率均随之增加,CO₂对CH₄的注置比却随之降低。在实验煤样变质程度范围内,CH₄置换率与煤变质程度和CO₂注置比均呈负相关关系。研究成果对井下注CO₂置换煤层CH₄的工程技术和理论具有指导意义。